Signal-to-Noise Eigenmode Analysis of the Two-Year COBE Maps

To test a theory of cosmic microwave background fluctuations, it is natural to expand an anisotropy map in an uncorrelated basis of linear combinations of pixel amplitudes --- statistically-independent for both the noise and the signal. These $S/N$-eigenmodes are indispensible for rapid Bayesian analyses of anisotropy experiments, applied here to the recently-released two-year COBE {\it dmr} maps and the {\it firs} map. A 2-parameter model with an overall band-power and a spectral tilt $\nu_{\Delta T}$ describes well inflation-based theories. The band-powers for {\it all} the {\it dmr} $53,90,31$ $a$+$b$ GHz and {\it firs} 170 GHz maps agree, $\{(1.1\pm 0.1)\times 10^{-5}\}^{1/2}$, and are largely independent of tilt and degree of (sharp) $S/N$-filtering. Further, after optimal $S/N$-filtering, the {\it dmr} maps reveal the same tilt-independent large scale features and correlation function. The unfiltered {\it dmr} $53$ $a$+$b$ index $\nu_{\Delta T}+1$ is $1.4\pm 0.4$; increasing the $S/N$-filtering gives a broad region at (1.0--1.2)$\pm$0.5, a jump to (1.4--1.6)$\pm$0.5, then a drop to 0.8, the higher values clearly seen to be driven by $S/N$-power spectrum data points that do not fit single-tilt models. These indices are nicely compatible with inflation values ($\sim$0.8--1.2), but not overwhelmingly so.Comment: submitted to Phys.Rev.Letters, 4 pages, uuencoded compressed PostScript; also bdmr2.ps.Z, via anonymous ftp to ftp.cita.utoronto.ca, cd to /pub/dick/yukawa; CITA-94-2

Constraints on Dark Energy from Supernovae, Gamma Ray Bursts, Acoustic Oscillations, Nucleosynthesis and Large Scale Structure and the Hubble constant

The luminosity distance vs. redshift law is now measured using supernovae and gamma ray bursts, and the angular size distance is measured at the surface of last scattering by the CMB and at z = 0.35 by baryon acoustic oscillations. In this paper this data is fit to models for the equation of state with w = -1, w = const, and w(z) = w_0+w_a(1-a). The last model is poorly constrained by the distance data, leading to unphysical solutions where the dark energy dominates at early times unless the large scale structure and acoustic scale constraints are modified to allow for early time dark energy effects. A flat LambdaCDM model is consistent with all the data.Comment: 19 pages Latex with 8 Postscript figure files. A new reference and constraint, w vs w' contour plots updated. Version accepted by the the Ap

Inhomogeneous reionization and the polarization of the cosmic microwave background

In a universe with inhomogeneous reionization, the ionized patches create a second order signal in the cosmic microwave background polarization anisotropy. This signal originates in the coupling of the free electron fluctuation to the quadruple moment of the temperature anisotropy. We examine the contribution from a simple inhomogeneous reionization model and find that the signal from such a process is below the detectable limits of the Planck Surveyor mission. However t he signal is above the fundamental uncertainty limit from cosmic variance, so th at a future detection with a high accuracy experiment on sub-arcminute scales is possible.Comment: 10 pages, 2 eps figures, final version accepted for publication in ApJ Letter

Constraining Large Scale Structure Theories with the Cosmic Background Radiation

We review the relevant 10+ parameters associated with inflation and matter content; the relation between LSS and primary and secondary CMB anisotropy probes; COBE constraints on energy injection; current anisotropy band-powers which strongly support the gravitational instability theory and suggest the universe could not have reionized too early. We use Bayesian analysis methods to determine what current CMB and CMB+LSS data imply for inflation-based Gaussian fluctuations in tilted $\Lambda$CDM, $\Lambda$hCDM and oCDM model sequences with age 11-15 Gyr, consisting of mixtures of baryons, cold (and possibly hot) dark matter, vacuum energy, and curvature energy in open cosmologies. For example, we find the slope of the initial spectrum is within about 5% of the (preferred) scale invariant form when just the CMB data is used, and for $\Lambda$CDM when LSS data is combined with CMB; with both, a nonzero value of $\Omega_\Lambda$ is strongly preferred ($\approx 2/3$ for a 13 Gyr sequence, similar to the value from SNIa). The $o$CDM sequence prefers $\Omega_{tot}<1$, but is overall much less likely than the flat $\Omega_\Lambda \ne 0$ sequence with CMB+LSS. We also review the rosy forecasts of angular power spectra and parameter estimates from future balloon and satellite experiments when foreground and systematic effects are ignored.Comment: 20 pages, LaTeX, 5 figures, 2 tables, uses rspublic.sty To appear in Philosophical Transactions of the Royal Society of London A, 1998. "Discussion Meeting on Large Scale Structure in the Universe," Royal Society, London, March 1998. Text and colour figures also available at ftp://ftp.cita.utoronto.ca/bond/roysoc9

Non-Gaussian Covariance of CMB B-modes of Polarization and Parameter Degradation

The B-mode polarization lensing signal is a useful probe of the neutrino mass and to a lesser extent the dark energy equation of state as the signal depends on the integrated mass power spectrum between us and the last scattering surface. This lensing B-mode signal, however, is non-Gaussian and the resulting non-Gaussian covariance to the power spectrum cannot be ignored as correlations between B-mode bins are at a level of 0.1. For temperature and E-mode polarization power spectra, the non-Gasussian covariance is not significant, where we find correlations at the 10^{-5} level even for adjacent bins. The resulting degradation on neutrino mass and dark energy equation of state is about a factor of 2 to 3 when compared to the case where statistics are simply considered to be Gaussian. We also discuss parameter uncertainties achievable in upcoming experiments and show that at a given angular resolution for polarization observations, increasing the sensitivity beyond a certain noise value does not lead to an improved measurement of the neutrino mass and dark energy equation of state with B-mode power spectrum. For Planck, the resulting constraints on the sum of the neutrino masses is ~ 0.2 eV and on the dark energy equation of state parameter we find, sigma_w ~ 0.5.Comment: 11 pages, 5 figures, minor changes, submitted to PR